Question

In: Finance

`1- Liz saved $270 at the end of every month for 6 years in her bank...

`1-

Liz saved $270 at the end of every month for 6 years in her bank account that earned 3.70% compounded monthly.

a. What is the accumulated value of her savings at the end of the period?

a$21,393.49

b$21,729.45

c$196,528.63

d$2,289.45

b. What is the interest earned over the period?

a$2,019.45

b$21,729.45

c$2,559.45

d$2,289.45

2-

What nominal interest rate compounded semi-annually is equivalent to 3.63% compounded quarterly?

%

3-If Lionel wants to earn interest of $3,547.75 on his $11,000.00 savings in 2 years, at what nominal interest rate compounded quarterly do you suggest he invests his money?

4-Orange Company holds a loan with an interest rate of 6.00% compounded quarterly. Calculate the effective rate of the loan.

Solutions

Expert Solution

Answer to Question 1:

Monthly Deposit = $270
Time Period = 6 years or 72 months

Annual Interest Rate = 3.70%
Monthly Interest Rate = 3.70% / 12
Monthly Interest Rate = 0.30833%

Accumulated Sum = $270*1.0030833^71 + $270*1.0030833^70 + … + $270*1.0030833 + $270
Accumulated Sum = $270 * (1.0030833^72 - 1) / 0.0030833
Accumulated Sum = $270 * 80.479362
Accumulated Sum = $21,729.45

Total Deposit = 72 * $270.00
Total Deposit = $19,440.00

Total Interest Earned = Accumulated Sum - Total Deposit
Total Interest Earned = $21,729.45 - $19,440.00
Total Interest Earned = $2,289.45

Answer to Question 2:

Annual Interest Rate = 3.63% compounded quarterly

Quarterly Interest Rate = 3.63% / 4
Quarterly Interest Rate = 0.9075%

Effective Annual Rate = (1 + Quarterly Interest Rate)^4 - 1
Effective Annual Rate = (1 + 0.009075)^4 - 1
Effective Annual Rate = 1.036797 - 1
Effective Annual Rate = 0.036797 or 3.6797%

Semiannual Interest Rate = (1 + Effective Annual Rate)^(1/2) - 1
Semiannual Interest Rate = (1 + 0.036797)^(1/2) - 1
Semiannual Interest Rate = 1.018232 - 1
Semiannual Interest Rate = 0.018232 or 1.8232%

Nominal Interest Rate compounded semiannually = 2 * Semiannual Interest Rate
Nominal Interest Rate compounded semiannually = 2 * 1.8232%
Nominal Interest Rate compounded semiannually = 3.6464% or 3.65%

jeff jeffy answered 1 year ago
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